Such a cleaning assembly is e.g. known from EP 536530. The known cleaning assembly contains a conveying device formed as an endless chain and comprises a plurality of accommodation means into which the bottles can be fitted. The bottles are then conveyed through the cleaning container in a freely suspended manner, said cleaning container being filled with a cleaning agent. To give the cleaning agent sufficient time to unfold its cleaning effect, the conveying device is guided within the cleaning container via a dwell time path, i.e. the conveying device is guided e.g. over spiral or helical paths prolonging the conveying path and thus the contact time with the cleaning agent. However, the bottles must remain completely submersed in the cleaning bath over the entire dwell time path, i.e. the cleaning bath requires a lot of space; and it has a considerable weight. Additionally, the cleaning agent must be kept in the entire cleaning container at an increased temperature, which requires enormous energy. Furthermore, a large amount of cleaning agent is required, which must be correctly disposed of after consumption.